I agree with that part of your statement but anything I can think of outside of mental issues that would be medically relevant to a physician would relate to use of firearms not ownership.
Such as diagnosing hearing problems or escalated lead levels in blood. Or I guess a dislocated shoulder because you're a pussy that couldn't handle the 10 gauge.
Other than that, if they are just being social engineering busy-bodies then screw em'.
Maybe an actual doctor could expand on the issue
dox??